A tank contains 10,000 gallons of a solution that is 5

5% of 10,000 = 500.

required %age = 500 * 100/7500 = 6.67%

I have a question.

Are we supposed to assume none of the sodium chloride was evaporated from the same original 10000 Gallons.

Hence of the 500 Gallons of original Sodium Chloride wouldn't the amount of sodium chloride in the solution also decrease by the same rate as the solution without Sodium Chloride?

We are told that from 10,000 gallons of a solution, evaporated 2,500 gallons of water. So, salt did not evaporate.

If it were the way you suggest (if salt evaporated at the same rate as the water) then the answer would simply be 5%.

This is a inverse proportional problem.

With the salt quantity remaining constant, if the water decreases, it means the percentage of salt increases.

\(\frac{10000}{7500} * 5\)

\(= \frac{20}{3}\)

= 6.67%

Answer = D

Initial amount of water must be 95% of total quantity (9500 gallons); as it's given that 5% (500 gallons) is sodium chloride. lf 2500 gallons of water evaporates, remaining solution should have 7000 gallons of water and 500 gallons of sodium chloride. Then we should have something like: 500/7000, which is clearly wrong.

Could someone please correct where l'm wrong?

Regards.

The remaining solution will be approximately what percent sodium chloride?

The remaining solution = 7000 gallons of water + 500 gallons of sodium chloride = 7500 gallons.

Answer: 500/7500.

We start with 10,000 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 10,000 = 500 gallons of sodium chloride.

When 2,500 gallons of water evaporate we are left with 7,500 gallons of solution. From here we can determine what percent of the 7,500 gallon solution is sodium chloride.

(sodium chloride/total solution) x 100 = ?

(500/7,500) x 100 = ?

5/75 x 100 = ?

1/15 x 100 = ?

100/15 = 20/3 = 6 2/3 = 6.67%

Answer is D.

Why did you take out 2500 from the 10000 gallons? The question said 2500 gallons of water, so why not 9500-2500, since 500g were sodium?

The solution is 10,000 gallons (9,500 gallons of water and 500 gallons of sodium chloride) out of which 2,500 gallons of water evaporates and we are left with 7,000 gallons of water and 500 gallons of sodium chloride, so total of 7,500 gallons.

Conceptually, it helps to remember that unless told otherwise, water is assumed to have zero percent sodium chloride (or zero percent alcohol, etc.).

The prompt refers to a solution that is 5 percent sodium chloride by volume. It's part water, part sodium chloride.

To make these numbers easier to work with, divide each original volume total by 100.

Let A = 100 gallons of 5 percent (=.05) sodium chloride solution

Let B = 25 gallons of water with zero percent (=0.0) sodium chloride

Resultant solution is A - B

(Concentration A)(Volume A) - (Concentration B)(Volume B) = (Resultant concentration of A - B)(Volume of resultant solution A - B)

In the equation below, arithmetically, LHS doesn't need the second term. It's just there to show that, in weighted average terms, it is being subtracted (it evaporates).

(.05)(100) - (0.0)(25) = \(\frac{x}{100}\)(100 - 25)

5 - 0 = \(\frac{75}{100}\)x

5 = \(\frac{3}{4}\)x

\(\frac{4}{3}\)*(5) = x

x = \(\frac{20}{3}\) = 6.67

Answer D

The remaining solution will be approximately what percent sodium chloride?" means: what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-2,500=7,500 gallons and sodium chloride is 500 gallons (5% of initial solution of 10,000 gallons) then sodium chloride is 500/7,500*100=~6.66% of the remaining solution of 7,500 gallons.

Answer: D.

To solve this problem, we need to determine the concentration of sodium chloride in the remaining solution after 2,500 gallons of water evaporate.

The initial volume of the solution is 10,000 gallons, and it is 5% sodium chloride by volume. This means that initially there are 5% of 10,000 gallons, or 0.05 * 10,000 = 500 gallons of sodium chloride in the solution.

When 2,500 gallons of water evaporate, the remaining volume of the solution is 10,000 - 2,500 = 7,500 gallons.

To find the concentration of sodium chloride in the remaining solution, we divide the amount of sodium chloride (500 gallons) by the remaining volume of the solution (7,500 gallons):

Concentration of sodium chloride = (Amount of sodium chloride / Remaining volume) * 100
Concentration of sodium chloride = (500 / 7,500) * 100
Concentration of sodium chloride = 0.0667 * 100
Concentration of sodium chloride ≈ 6.67%

Therefore, the remaining solution will be approximately 6.67% sodium chloride.

The correct answer is (D) 6.67%.